When Napoleon took the reins of government, he decided to call himself an emperor rather than a king. Emperor is a temporal title, it's not intended to be passed down to heirs the same way a throne is. French emperors rule at the will of the people, and it's up to them to decide whether they want a monarch or not.
Napoleon III, the last French monarch, was captured during the Franco-Prussian war, and after his death, the French decided they'd had enough of monarchs and the third French republic lasted until WWII. It was replaced by the Germans with Vichy, and then after the war, the fourth and fifth republics.
It's highly unlikely that the French will ever accept another monarch. There are Bonapartist and a Orléanist (Bourbon) pretenders to the throne, but none hold any public office. If the government falls apart again like it did in 1958, it should be replaced with another republic as it was then. Nobody can really rule out a third French empire, but the trend of democracy worldwide has been towards devolution of power rather than centralization, France is more likely to break apart than it is to re-imperialize.
